Prime-Enforced Helical Symmetry Constraints in Thermodynamic Emergence of Electromagnetism: Engineering Tunable Self-Organized Superconducting Shells via the Radial Helical Gear Condenser in Hybrid Layered Composites

This work establishes that the complete set of Maxwell’s equations and the dynamics of the electromagnetic field emerge deductively as a theorem from the three primitive axioms of the Zeta-Minimizer Theorem (ZMT). Starting from the helical transfer matrix in star topology with anchor prime 19 and applying the integer gear up to its prime rule, the grand-partition function is uniquely constructed. Critical compositions in the s→0 limit fix the per-gear constants C_k, which govern the interaction parameters and the full Lyapunov spectrum. Thermodynamic continuity at interfaces of differing gear content then enforces the matching condition that recovers Maxwell’s equations and the electromagnetic field dynamics from first principles via the covariant fugacity Hessian. As the principal engineering realization, the Radial Helical Gear Condenser (RHGC) is introduced, a self-regulating cylindrical membrane whose hybrid layered polymer–metal composite architecture enables precise radial pressure-gradient tuning. This spontaneously forms a thin, controllable shell of marginal stability (λ_(k,19)=0). The results provide a thermodynamic origin for electromagnetism and a versatile, first-principles pathway to high-temperature superconductivity and advanced materials design.